8.
Selection strategy for ﬁxing nodes in FETI-DP method
FETI-DP Method
Fixing Nodes
Deﬁnition of Fixing Nodes
Problem with deﬁnition of ﬁxing nodes in the case of non-regular
meshes which are decomposed by a mesh decomposer (e.g.
METIS, http://glaros.dtc.umn.edu/gkhome/views/metis).
Minimal number of ﬁxing nodes due to the nonsingular matrix of
subdomains
Theoretically the number of ﬁxing node = the number of all
nodes on boundaries

14.
Selection strategy for ﬁxing nodes in FETI-DP method
Algorithm for Fixing Node Selection in 2D
Algorithm for Fixing Node Selection in 2D
Deﬁnition of Boundary Curves
Boundary curve connect boundary nodes between two ﬁxing nodes.
Fixing nodes can be added into:
Centroid of boundary curve
Each n-th member of the boundary curve
Each n-th end of the part of the boundary curve
“Integral points” of the boundary curve
Random position y
x

21.
Selection strategy for ﬁxing nodes in FETI-DP method
Algorithm for Fixing Node Selection in 3D
Algorithm for Fixing Node Selection in 3D
Deﬁnition of Edges and Sufraces
Edge - deﬁned by boundary nodes which belongs to more than two
subdomains
Surface - deﬁned by boundary nodes which belongs to exactly two
subdomains

22.
Selection strategy for ﬁxing nodes in FETI-DP method
Algorithm for Fixing Node Selection in 3D
Algorithm for Fixing Node Selection in 3D
Deﬁnition of Edges and Sufraces
Edge - deﬁned by boundary nodes which belongs to more than two
subdomains
Surface - deﬁned by boundary nodes which belongs to exactly two
subdomains

27.
Selection strategy for ﬁxing nodes in FETI-DP method
Numerical Tests of Algorithm for 3D
Cube - 27000 elements
Results of Tests - The Number of Iterations with Respect to the Number of Fixing Nodes

28.
Selection strategy for ﬁxing nodes in FETI-DP method
Numerical Tests of Algorithm for 3D
Cube - 27000 elements
Results of Tests - Time of Condensation with Respect to the Number of Fixing Nodes

29.
Selection strategy for ﬁxing nodes in FETI-DP method
Numerical Tests of Algorithm for 3D
Cube - 27000 elements
Results of Tests - Total Time of the Solution with Respect to the Number of Fixing Nodes

30.
Selection strategy for ﬁxing nodes in FETI-DP method
Numerical Tests of Algorithm for 3D
Cube - 64000 elements
Results of Tests - The Number of Iterations with Respect to the Number of Fixing Nodes

31.
Selection strategy for ﬁxing nodes in FETI-DP method
Numerical Tests of Algorithm for 3D
Cube - 64000 elements
Results of Tests - Time of Condensation with Respect to the Number of Fixing Nodes

32.
Selection strategy for ﬁxing nodes in FETI-DP method
Numerical Tests of Algorithm for 3D
Cube - 64000 elements
Results of Tests - Total Time of the Solution with Respect to the Number of Fixing Nodes

34.
Selection strategy for ﬁxing nodes in FETI-DP method
Conclusions and Future Works
Conclusions and Future Works
The algorithm for selection of ﬁxing nodes for arbitrary 2D mesh
has been developed
Increasing of the number of the ﬁxing nodes leads to decreasing
of the number of iterations in coarse problem and its time of the
solution
Big number of ﬁxing nodes leads to prolongation of the whole
time of the solution
Developing of the algorithm for the selection of ﬁxing nodes for
regular 3D mesh
Optimization of the algorithm

35.
Selection strategy for ﬁxing nodes in FETI-DP method
Acknowledgement
Acknowledgement
Thank you for your attention.
Financial support for this work was provided by project number
103/09/H078 of the Czech Science Foundation. The ﬁnancial support
is gratefully acknowledged.